The Origins of Infinitesimal Calculus

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Author: Margaret E. Baron

Publisher: Elsevier

ISBN: 1483280926

Category: Mathematics

Page: 312

View: 2548

The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

The Historical Development of the Calculus

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Author: C.H.Jr. Edwards

Publisher: Springer Science & Business Media

ISBN: 1461262305

Category: Mathematics

Page: 368

View: 8885

The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.

Elementary Calculus

An Infinitesimal Approach

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Author: H. Jerome Keisler

Publisher: Courier Corporation

ISBN: 0486484521

Category: Mathematics

Page: 913

View: 6388

This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

A Primer of Infinitesimal Analysis

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Author: John L. Bell

Publisher: Cambridge University Press

ISBN: 0521887186

Category: Mathematics

Page: 124

View: 5218

A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

Infinitesimal calculus

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Author: Jean Alexandre Dieudonné

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 427

View: 5689

Infinitesimal

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Author: Amir Alexander

Publisher: Oneworld Publications

ISBN: 1780745338

Category: Science

Page: 368

View: 4598

On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.

Applied Nonstandard Analysis

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Author: Martin Davis

Publisher: Courier Corporation

ISBN: 0486152340

Category: Mathematics

Page: 208

View: 7555

This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

The Metaphysical Principles of the Infinitesimal Calculus

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Author: René Guénon

Publisher: Sophia Perennis

ISBN: 9780900588129

Category: Mathematics

Page: 132

View: 2985

Rene Guenon (1886-1951) is undoubtedly one of the luminaries of the twentieth century, whose critique of the modern world has stood fast against the shifting sands of recent philosophies. His oeuvre of 26 volumes is providential for the modern seeker: pointing ceaselessly to the perennial wisdom found in past cultures ranging from the Shamanistic to the Indian and Chinese, the Hellenic and Judaic, the Christian and Islamic, and including also Alchemy, Hermeticism, and other esoteric currents, at the same time it directs the reader to the deepest level of religious praxis, emphasizing the need for affiliation with a revealed tradition even while acknowledging the final identity of all spiritual paths as they approach the summit of spiritual realization. Guenon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet threat throughout his doctrinal studies. In this late text published just five years before his death, Guenon devotes an entire volume to questions regarding the nature of limits and the infinite, both with respect to the calculus as a mathematical discipline, and to the symbolism of the initiatic path. This book therefore extends and complements the geometrical symbolism Guenon employs in several of his other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. A sampling of chapter titles will convey some sense of this remarkable work: 'Infinite and Indefinite', 'Degrees of Infinity', 'Zero is not a Number', 'The Law of Continuity', 'Vanishing Quantities', 'Various Orders of Indefinitude', 'The Arguments of Zeno of Elea', 'The True Conception of Passage to the Limit'. The Collected Works of Rene Guenon brings together the writings of one of the greatest prophets of our time, whose voice is even more important today than when he was alive. Huston Smith, author of The World's Religions, etc.

A Treatise on Infinitesimal Calculus

Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics. The dynamics of material systems

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Author: Bartholomew Price

Publisher: N.A

ISBN: N.A

Category: Calculus

Page: 579

View: 745

Lectures on the Hyperreals

An Introduction to Nonstandard Analysis

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Author: Robert Goldblatt

Publisher: Springer Science & Business Media

ISBN: 1461206154

Category: Mathematics

Page: 293

View: 6201

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.

The Tangled Origins of the Leibnizian Calculus

A Case Study of a Mathematical Revolution

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Author: Richard C. Brown

Publisher: World Scientific

ISBN: 9814390798

Category: Mathematics

Page: 310

View: 7049

1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.

Nonstandard Analysis

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Author: Alain Robert

Publisher: Courier Corporation

ISBN: 9780486432793

Category: Mathematics

Page: 156

View: 8444

This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.

A Treatise on Infinitesimal Calculus, Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics: Differential calculus. 1857.- v.2. Integral calculus, calculus of variations, and differential equations. 1865.- v.3. Statics and dynamics of material particles. 1856.- v.4. The dynamics of material systems. 1862

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Author: Bartholomew Price

Publisher: N.A

ISBN: N.A

Category: Calculus

Page: N.A

View: 416